Resonance in Elemental Benzenoids

The phenomenon of resonance amongst a set of different classical chemical structures entails at an elementary level the enumeration of these resonance structures, corresponding (in benzenoid molecules) to perfect matchings of the underlying molecular (n-network) graph. This enumeration is analytically performed here for the finite-sized elemental benzenoid graphs corresponding to hexagonal coverings on suitable closed surfaces, namely the torus and the Klein bottle. Relevance is also indicated for a class of benzenoid structures corresponding to cylinders with polyhex coverings on the sides (but not the “ends”).